There are a few reasons or causes for this type of problem one that comes to my mind with those vehicles is the starter solenoid.It can actually draw a very small amount of constant power due to an internal fault within itself although the ignition isn't even turned on.
Another cause could be a car alarm that is over drawing power or a stereo that has internal faults.
Have you've gone through the fuse boxes and checked to see if any of the fuses or relays etc have rusty or corroded connections or sockets?Plus there could be a circuit with a frayed , bare or burnt or shorted out wire in one of the harness's.
You mentioned that you hardly ever use that vehicle so I must ask you under what temperatures or environment conditions and for how long on the average does it sit?
Another thing is just bec it's a new battery doesn't mean that it's actually a real good reliable solid battery. What cold cranking amp rating does that battery have?Also when you changed the battery cables did you clean the starter , alternator , engine block ground, ground posts?The No1 reason for any vehicles electrical failers or faults are bad grounds.
I'd try checking the voltage coming out of the battery with the engine off then when it's running and comparing the two different voltages.Basically you should have 12.7 or so volts without the engine running then from 13.7 to over 14 volts with the engine running.
One test you could do is use a volt meter set at 20 volts and with the engine off read the battery's current rating then one by one remove the fuses and as the fuse is out check the battery's voltage output level.If you suddenly notice that the current is greater with any fuse out , find out what circuit that is and figure out if that is a circuit that is drawing current with the ignition off.Example the radio feed circuit for the constant 12 volts would obviously be the one thing that draws power or an alarm system.
Hope that helps and best of luck.By the way if you've not changed the starter solenoid in awhile I'd start there bec it can draw the most if defective.Also even a bad voltage regulator could cause a minor short and due to most stereo's having a need for a constant 12 volt feed the regulator or the connections could be at fault.
Keep in mind that in order to have any engine really get enough cranking amps from a battery the battery should be rated at about 5 times the engines required cranking cramp rating.Example a big GM full size 8 cylinder vehicle really only has about 165 cranking amp rating but in order to make sure due to weather or extreme temperatures or a battery cells sitting not being used or charged daily etc it's best really to have a good 850 cold cranking amp battery.
